Yahoo said Thursday afternoon that Microsoft has refused to buy Yahoo for $33 a share, the price Microsoft offered May 3 and then pulled off the table when Yahoo’s co-founders held out for $37. Microsoft refusal makes its “strategic clarity” suspect.

Yahoo, in turn, refused to sell Microsoft just its search business, which Microsoft was willing to buy. No terms were disclosed but Microsoft claims Yahoo could have made a kiling.

With nothing left to talk about, all negotiations are off, Yahoo said, sending its shares reeling. They closed down 10% to $23.36 after being down 13% or ~$3.50 to $22.70, closer to where it was 19 weeks ago when Microsoft entered the scene. The stock has been artificially propped up ever since on speculation a deal would be cut.

Conversely Microsoft shares rose ~4% to $28.25, up $1.12 cents on the news that it wouldn’t have to spend all that money and cope with integrating an unfriendly and flagging prize.

With Microsoft apparently out of the picture – even if Microsoft in a prepared statement said it’s still willing to do a partial deal for more money than Yahoo can dream about this second – Yahoo stuck its head in the lion’s mouth and announced an advertising-search deal with Google, which seems on the face of it a horrific outcome for Microsoft, which reportedly offered $40 a share for Yahoo a year ago.

Of course any Yahoo-Google deal has to clear antitrust scrutiny and the waterhole poisoning of Microsoft lobbyists.

A Wall Street Journal blog observed that “Yahoo destroyed itself to save itself. Microsoft tried to get stronger, but only ended up exposing its own weakness. Somehow Google emerged triumphant, effectively neutralizing its two biggest competitors.

“That is what makes the Yahoo-Microsoft non-merger such a spectacular failure. Never have so few failed so many for so much at stake.”

In the statement Yahoo released Thursday it said discussions concluded after “numerous meetings and conversations with Microsoft regarding a number of transaction alternatives, including a meeting between Yahoo! and Microsoft on June 8th [Sunday] in which chairman Roy Bostock and other independent board members from Yahoo! participated. At that meeting, Microsoft representatives stated unequivocally that Microsoft is not interested in pursuing an acquisition of all of Yahoo!, even at the price range it had previously suggested.

“With respect to an acquisition of Yahoo!’s search business alone that Microsoft had proposed, Yahoo!’s board of directors has determined, after careful evaluation, that such a transaction would not be consistent with the company’s view of the converging search and display marketplaces, would leave the company without an independent search business that it views as critical to its strategic future and would not be in the best interests of Yahoo! stockholders.

“Yahoo! remains focused on maximizing value for stockholders by continuing to execute on its strategy of being the ‘starting point’ for the most consumers on the Internet and a ‘must buy’ for advertisers. The online advertising industry is projected to grow from $40 billion in 2007 to approximately $75 billion in 2010 and the company believes it has the right assets, strategic plan, board of directors and management team to capitalize on this growth opportunity.”

There has been no public reaction yet from billionaire corporate raider Carl Icahn – (the calm before the storm?); he wasn’t coming to the phone for anybody. Yesterday at least Icahn owned >4% of Yahoo and was embarked on a proxy fight to unseat the Yahoo board. He was banking on Microsoft buying the joint.

One would think that he’s going to want copies of the notes on the back and forth between Microsoft and Yahoo. And he’s going to want to plum the depths of Microsoft saying that it believes its alternative proposal for Yahoo “would have delivered in excess of $33 per share to the Yahoo shareholders.”

Microsoft’s full statement reads, “In the weeks since Microsoft withdrew its offer to acquire Yahoo!, the two companies have continued to discuss an alternative transaction that Microsoft believes would have delivered in excess of $33 per share to the Yahoo! shareholders. This partnership would ensure healthy competition in the marketplace, providing greater choice and innovation for advertisers, publishers and consumers.

“As stated on May 3rd and reiterated on May 18th Microsoft was not interested in rebidding for all of Yahoo!. Our alternative transaction remains available for discussion.”